This dissertation consists of three related chapters that study financial market volatility, jumps and the economic factors behind them. Each of the chapters analyzes a different aspect of this problem. The first chapter examines tests for jumps based on recent asymptotic results. Monte Carlo evidence suggests that the daily ratio z-statistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump classification probabilities. Theoretical and Monte Carlo analysis indicate that microstructure noise biases the tests against detecting jumps, and that a simple lagging strategy corrects the bias. Empirical work documents evidence for jumps that account for seven percent of stock market price variance. Building on realized variance and bi-power variation measures constructed from high-frequency financial prices, the second chapter proposes a simple reduced form framework for modelling and forecasting daily return volatility. The chapter first decomposes the total daily return variance into three components, and proposes different models for the different variance components: an approximate long-memory HAR-GARCH model for the daytime continuous variance, an ACH model for the jump occurrence hazard rate, a log-linear structure for the conditional jump size, and an augmented GARCH model for the overnight variance. Then the chapter combines the different models to generate an overall forecasting framework, which improves the volatility forecasts for the daily, weekly and monthly horizons. The third chapter studies the economic factors that generate financial market volatility and jumps. It extends the recent literature by separating market responses into continuous variance and discontinuous jumps, and differentiating the market’s disagreement and uncertainty. The chapter finds that there are more large jumps on news days than on no-news days, with the fixed-income market being more responsive than the equity market, and non-farm payroll employment being the most influential news. Surprises in forecasts impact volatility and jumps in the fixed-income market more than the equity market, while disagreement and uncertainty influence both markets with different effects on volatility and jumps. JEL classification: C1, C2, C5, C51, C52, F3, F4, G1, G14 / Dissertation

In this dissertation we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conservative form and present a convergence analysis for the two-dimensional Black-Scholes equation arising in the Hull-White model for pricing European options with stochastic volatility. We formulate a non-conforming Petrov-Galerkin finite element method with each basis function of the trial space being determined by a set of two-point boundary value problems defined on element edges. We show that the bilinear form of the finite element method is coercive and continuous and establish an upper bound of order O(h) on the discretization error of method, where h denotes the mesh parameter of the discretization. We then present a finite volume method for the resulting equation, based on a fitting technique proposed for a one-dimensional Black-Scholes equation. We show that the method is monotone by proving that the system matrix of the discretized equation is an M-matrix. Numerical experiments, performed to demonstrate the usefulness of the method, will be presentd.

This dissertation collects two papers regarding the econometric and economic theory and testing of the predictability of asset returns. It is widely accepted that stock returns are not only predictable but highly so. This belief is due to an abundance of existing empirical literature fi nding often overwhelming evidence in favor of predictability. The common regressors used to test predictability (e.g., the dividend-price ratio for stock returns) are very persistent and their innovations are highly correlated with returns. Persistence when combined with a correlation between innovations in the regressor and asset returns can cause substantial over-rejection of a true null hypothesis. This result is both well documented and well known. On the other hand, stochastic volatility is both broadly accepted as a part of return time series and largely ignored by the existing econometric literature on the predictability of returns. The severe e ffect that stochastic volatility can have on standard tests are demonstrated here. These deleterious e ffects render standard tests invalid. However, this problem can be easily corrected using a simple change of chronometer. When a return time series is read in the usual way, at regular intervals of time (e.g., daily observations), then the distribution of returns is highly non-normal and displays marked time heterogeneity. If the return time series is, instead, read according to a clock based on regular intervals of volatility, then returns will be independent and identically normally distributed. This powerful result is utilized in a unique way in each chapter of this dissertation. This time-deformation technique is combined with the Cauchy t-test and the newly introduced martingale estimation technique. This dissertation nds no evidence of predictability in stock returns. Moreover, using martingale estimation, the cause of the Forward Premium Anomaly may be more easily discerned.

Affine term structure models (ATSMs) are known to have a trade-off in predicting future Treasury yields and fitting the time-varying volatility of interest rates. First, I empirically study the role of macroeconomic variables in simultaneously achieving these two goals under affine models. To this end, I incorporate a liquidity demand theory via a measure of the velocity of money into affine models. I find that this considerably reduces the statistical tension between matching the first and second moments of interest rates. In terms of forecasting yields, the models with the velocity of money outperform among the ATSMs examined, including those with inflation and real activity. My result is robust across maturities, forecasting horizons, risk price specifications, and the number of latent factors. Next, I incorporate latent macro factors and the spread factor between the short-term Treasury yield and the federal funds rate into an affine term structure model by imposing cross-equation restrictions from no-arbitrage using daily data. In doing so, I identify the highfrequency monetary policy rule that describes the central bank's reaction to expected inflation and real activity at daily frequency. I find that my affine model with macro factors and the spread factor shows better forecasting performance.

This study includes three issues about the dynamic of 30-days Taiwan Commercial Paper rate (CP2).The first issue focuses on the estimation of continuous-time short-term interest rate models. We discretize the continuous-time models by using two different approaches, and then use weekly and monthly data to estimate the parameters. The models are evaluated by data fit. We find that the estimated parameters are similar for different discretization approaches and would be more stable and efficient under quasi-maximum likelihood (QML) with weekly data. There exists mean reversion for Taiwan CP rate and the relationship between the volatility and the level of interest rates are less than 1 and smaller than that of American T-Bill rates reported by CKLS (1992) and Nowman (1997). We also find that CIR-SR model performs best for Taiwan CP rate. The second issue compares the continuous-time short-term interest rate models empirically both by predictive accuracy test and encompassing test. Having the estimated parameters of the models by discretization of Nowman(1997) and QML, we produce the forecasts on conditional mean and volatility for the interest rate over multiple-step-ahead horizons. The results indicate that the sophisticated models outperform the simpler models in the in-sample data fit, but have a distinct performance in the out-of-sample forecasting. The models equipped with mean reversion can produce better forecasts on conditional means during some period, and the heteroskedasticity variance model with outperform counterparts in volatility forecasting in some periods. The third issue concerns the persistent and massive volatility of short-term interest rates. This part inquires how the realizations on Taiwan short-term interest rates can be best described empirically. Various popular volatility specifications are estimated and tested. The empirical findings reveal that the mean reversion is an important characteristic for the Taiwan interest rates, and the level effect exists. Overall, the GARCH-L model fits well to Taiwan interest rates.

We present two option pricing models, both different from the classical Black-Scholes-Merton model. The first model, suggested by Heston, considers the case where the asset price volatility is stochastic. For this model we study the asset price process and give in detail the derivation of the European call option price process. The second model, suggested by Brody-Hughston-Macrina, describes the observation of certain information about the claim perturbed by a noise represented by a Brownian bridge. Here we also study in detail the properties of this noisy information process and give the derivations of both asset price dynamics and the European call option price process.

This thesis presents the modeling of credit risk by using structural approach. Three fundamental questions of credit risk literature are analyzed throughout the research: modeling single firm credit risk, modeling portfolio credit risk and credit risk pricing. First we analyze these questions under the assumptions that firm value follows a geometric Brownian motion and the interest rates are constant. We discuss the weaknesses of the geometric brownian motion assumption in explaining empirical properties of real data. Then we propose a new extended model in which asset value, volatility and interest rates follow affine jump diffusion processes. In our extended model volatility is stochastic, asset value and volatility has correlated jumps and interest rates are stochastic and have jumps. Finally, we analyze the modeling of single firm credit risk and credit risk pricing by using our extended model and show how our model can be used as a solution for the problems we encounter with simple models.

Ce travail de thèse poursuit une perspective double dans l'usage conjoint des méthodes de Monte Carlo séquentielles (MMS) et de l'algorithme Espérance-Maximisation (EM) dans le cadre des modèles de Markov cachés présentant une structure de dépendance markovienne d'ordre supérieur à 1 au niveau de la composante inobservée. Tout d'abord, nous commençons par un exposé succinct de l'assise théorique des deux concepts statistiques à travers les chapitres 1 et 2 qui leurs sont consacrés. Dans un second temps, nous nous intéressons à la mise en pratique simultanée des deux concepts au chapitre 3 et ce dans le cadre usuel où la structure de dépendance est d'ordre 1. L'apport des méthodes MMS dans ce travail réside dans leur capacité à approximer efficacement des fonctionnelles conditionnelles bornées, notamment des quantités de filtrage et de lissage dans un cadre non linéaire et non gaussien. Quant à l'algorithme EM, il est motivé par la présence à la fois de variables observables et inobservables (ou partiellement observées) dans les modèles de Markov Cachés et singulièrement les mdèles de volatilité stochastique étudié. Après avoir présenté aussi bien l'algorithme EM que les méthodes MCs ainsi que quelques unes de leurs propriétés dans les chapitres 1 et 2 respectivement, nous illustrons ces deux outils statistiques au travers de la calibration d'un modèle de volatilité stochastique. Cette application est effectuée pour des taux change ainsi que pour quelques indices boursiers au chapitre 3. Nous concluons ce chapitre sur un léger écart du modèle de volatilité stochastique canonique utilisé ainsi que des simulations de Monte Carlo portant sur le modèle résultant. Enfin, nous nous efforçons dans les chapitres 4 et 5 à fournir les assises théoriques et pratiques de l'extension des méthodes Monte Carlo séquentielles notamment le filtrage et le lissage particulaire lorsque la structure markovienne est plus prononcée. En guise d'illustration, nous donnons l'exemple d'un modèle de volatilité stochastique dégénéré dont une approximation présente une telle propriété de dépendance.

This paper puts forward a Bayesian Global Vector Autoregressive Model with Common Stochastic Volatility (B-GVAR-CSV). We assume that Country specific volatility is driven by a single latent stochastic process, which simplifies the analysis and implies significant computational gains. Apart from computational advantages, this is also justified on the ground that the volatility of most macroeconomic quantities considered in our application tends to follow a similar pattern. Furthermore, Minnesota priors are used to introduce shrinkage to cure the curse of dimensionality. Finally, this model is then used to produce predictive densities for a set of macroeconomic aggregates. The dataset employed consists of quarterly data spanning from 1995:Q1 to 2012:Q4 and includes 45 economies plus the Euro Area. Our results indicate that stochastic volatility specifications influences accuracy along two dimensions: First, it helps to increase the overall predictive fit of our model. This result can be seen for some variables under scrutiny, most notably for real GDP and short-term interest rates. Second, it helps to make the model more resilient with respect to outliers and economic crises. This implies that when evaluated over time, the log predictive scores tend to show significantly less variation as compared to homoscedastic models. (author's abstract) / Series: Department of Economics Working Paper Series

In the original Vasicek model interest rates are calculated assuming that volatility remains constant over the period of analysis. In this study, we constructed a stochastic volatility model for interest rates. In our model we assumed not only that interest rate process but also the volatility process for interest rates follows the mean-reverting Vasicek model. We derived the density function for the stochastic element of the interest rate process and reduced this density function to a series form. The parameters of our model were estimated by using the method of moments. Finally, we tested the performance of our model using the data of interest rates in Turkey.